Discuss, with necessary theory, how is interference pattern in Young's double slit experiment modified when a thin glass plate is introduced in the path of one of the interference waves?

In Young’s double-slit experiment, an interference pattern arises due to the superposition of coherent light waves from the two slits. The condition for constructive interference is given by dsin⁡θ=mλd \sin \theta = m \lambda, and for destructive interference, dsin⁡θ=(m+12)λd \sin \theta = (m + \frac{1}{2}) \lambda, where dd is the slit separation, θ\theta is the angular position, mm is ______ ___ _________ __________ ____ _____ _______ ___.
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